Computational and Theoretical Chemistry

Computational and Theoretical Chemistry 976 (2011) 148 152 Contents lists available at SciVerse ScienceDirect Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc Computational outlook on the ribosome as an entropy trap Hadieh Monajemi a,, Sharifuddin Mohd Zain b, Wan Ahmad Tajuddin Wan Abdullah a,c a Department of Physics, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia b Department of Chemistry, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia c Faculty of Computer Science and Information Technology, Universiti Malaya, 50603 Kuala Lumpur, Malaysia article info abstract Article history: Received 17 July 2011 Received in revised form 15 August 2011 Accepted 15 August 2011 Available online 23 August 2011 Keywords: Transition state Peptide bond formation Ribosome Density Functional Theory Recent progress in the study of transition structure of peptide bond formation indicates that ribosome acts as a water trap. However, considering experimental approaches, it is hard to overlook the role of ribosomal bases in catalyzing the reaction by substrate stabilization. In this study, we employ ab initio quantum chemistry methods to calculate the transition structure of the peptide bond formation in the absence of ribosomal bases. This will allow us to compare the transition structure in the process with the ones obtained computationally in the presence of ribosomal bases, and also the reaction rate with the experimental results. To save calculation time this study was carried out using short fragments of the A and P site aminoacyl-trnas. Based on our observation, the absence of ribosome results in a more favorable enthalpy but a less favorable entropy. Overall, the lower rate of reaction compared to that in the ribosomal environment indicates the role of ribosomal bases in catalyzing the reaction entropically. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction The process of ester bond dissociation and peptide bond formation on the ribosome occur simultaneously with the protonation of the A76 3 0 leaving group from the P-site peptidyl-trna and deprotonation of the attacking nucleophile from the A-site aminoacyltrna. It is believed that the principles of ribosomal catalysis are different from those of other ordinary enzymes, based on thermodynamic studies of the transition state of the process [1,2]. It was suggested experimentally by Sievers et al. [2] and Bieling et al. [3] that the catalytic role of the ribosome is due to substrate stabilization in the PTC (Peptidyl Transferase Center) rather than an acid base mechanism; the higher activation entropy at the active site of the ribosome compared to that in bulk water reveals that the ribosome acts as an entropy trap. Wallin and Åqvist [4] on the other hand, based on computational studies, proposed another model for the transition structure of the peptide bond formation in which the ribosome acts as a water trap. Their study was consistent with Rhodes et al. s molecular dynamics (MD) simulations in which several water molecules enter the hairpin ribozyme cavity and form a string of water molecules [5]. Being solvent protected, the cavity area in the ribozyme is small enough to discriminate against the large water clusters and allow only a few water molecules to enter the site. Additional to the importance of the trapped water molecules by ribosomal bases in the active site, Wallin and Åqvist proposed a model in Corresponding author. E-mail address: h.monajemi@hotmail.com (H. Monajemi). which the ribosomal bases do not directly participate in the chemical reaction; however, they employ water molecules to act as proton shuttles between the 2 0 and 3 0 groups in the P-site A76 base leading to eight-membered transition structures (Fig. 1a). Absence of the water molecules results in high enthalpy barriers with unfavorable entropies of activation. The model then claims, the higher activation entropy with presence of water molecules compared to that for the six-membered transition structure (Fig. 1b), renders the conception of the ribosome as an entropy trap insignificant. In order to figure out the actual role of the ribosome in the catalysis, we employed computational methods to study the transition structure of the peptide bond formation in the absence of both water molecules and ribosomal bases as a comparison to the experimental studies of Sievers et al. in ribosome and solution and the computational studies of Gindulyte et al. with ribosomal bases [6]. Gindulyte et al. carried out studies in which the transition structure is optimized with respect to a frozen ribosomal environment, whilst we have optimized the transition structure as an uncatalyzed peptide bond formation. Therefore, the difference in the transition structure between these two studies should indicate the role played by ribosomal bases in stabilizing the structure forming the peptide bond. The amino acid side chain used in this study is alanine since it has been widely used in previous computational studies in investigating the process of peptide bond formation [6 9]. Unlike the study carried out by Thirumoorthy and Nandi [8] in which the process of peptide bond formation does not include the sugar moiety, we have used sugar moieties as the short fragment of the A and P site trna molecules to mimic the actual process in which the ester 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.08.017

H. Monajemi et al. / Computational and Theoretical Chemistry 976 (2011) 148 152 149 Fig. 1. (a) Eight-membered transition structure, and (b) six membered transition structure. bond dissociation and peptide bond formation occur simultaneously. 2. Methods Computational quantum chemistry calculations were used to optimize the structure of the transition state. For computational economy, sugar moieties were used to replace the trna chains, leaving only those fragments containing the atoms which are essential and sufficient for the process of ester bond dissociation and peptide bond formation. Bond breaking and bond forming calculations require both accuracy and speed, and post Hartree Fock methods are very time consuming [10,11]. Of course, the high accuracy and low computational cost of the MP2 (second order Møller Plesset perturbation theory) method would tempt one to employ it in the current work; however, it is observed that this method failed at longer distances [12,13]. The DFT (Density Functional Theory) method is less expensive than the MP2 method (the cost of which scales as the third power of the system size while the MP2 method scales as the fifth power of the system size) and it seems to be relatively more accurate at longer distances (based on previous comparison calculations for the most suitable method to study the bond breaking/forming process) [12]. Furthermore, the previous studies have indicated that after including the diffuse function in the basis set, the DFT method using the hybrid Becke three-parameter functional with the correlation functional of Lee, Yang, and Parr (B3LYP) can be as efficient and realistic as the MP2 method in predicting the electronic structure of organic compounds [7]. In addition, harmonic vibrational frequencies and derived thermochemical quantities obtained at the MP2 level are not as reliable as those obtained from the B3-based DFT procedures [14,15]. Thus, we employed the DFT/B3LYP method to optimize our structure to the transition state [16]. To consider accurate representation of bonding between atoms, split valance basis set with two polarization functions and one diffuse function i.e. 6-31+G(d,p) were used [7,11]. The QST (Quadratic synchronous transit) method from STQN (Synchronous Transit Quasi-Newton) algorithm was used for the optimization. The QST2 (QST with two input structures: reactants and products) method used yielded an initial optimal transition state which was then used as the starting transition state structure to be re-optimized using the Berny algorithm [17]. Using vibrational eigenmodes the energy of activation from the reactants to the transition state was calculated. This enables the calculation of the reaction rate constant using the Eyring equation (Eq. (1)) from transition state theory. k ¼ðk B T=hÞ expð DG z =RTÞ Using this method, the rate of peptide bond formation for the alanine dipeptide was calculated. All optimizations were carried out at the constant temperature of 298.15 K and pressure of 1 atm using the Gaussian03 [17] suite of programs. 3. Results and discussion The initial structure and the method of calculation in our study are similar to that of Gindulyte et al. However, Gindulyte et al. optimized the structure in frozen ribosomal environment whereas we optimized the same structure in vacuum. As suggested by Dorner et al., the P-site A 76 2 0 -OH group contributes to the process of peptidyl transferase by protonation of the P-site A76 3 0 leaving group and deprotonation of the A-site attacking nucleophile [18,19], leading to a six-membered transition structure (Fig. 1b). Our transition state calculations on the other hand, has led to a ð1þ

150 H. Monajemi et al. / Computational and Theoretical Chemistry 976 (2011) 148 152 Fig. 2. The 4-membered transition structure of the peptide bond formation and the ester bond dissociation in our study. four-membered transition structure (similar to Gindulyte et al. s study [6]) where the P-site A 76 2 0 -OH group plays no role in the proton shuttle mechanism (Fig. 2). In the optimized four-membered transition structure, this group forms a hydrogen bond with the P-site amino acid s carboxylic oxygen in our study (Fig. 2) whereas, the same hydrogen bond is formed with the A-site amino acid in Gindulyte et al. s study [6]. This is the main difference in the overall geometry of the transition structure in the two studies, while the ester bond dissociation and peptide bond formation occur at the same length in both studies (Table 1). Although both studies lead to four-membered transition structures, the high activation energy in our study (Fig. 3) (53.1 kcal/mol compared to 35.5 kcal/mol) reveals a comparatively unfavorable reaction rate. The higher energy barrier obtained in our study can be due to the inhibitory hydrogen bond to the P-site amino acid (Fig. 2 (V)), which is not observed in Gindulyte et al. s study. In their study, when the geometry is restricted in the frozen ribosomal environment, the corresponding hydrogen bonds to the A- site amino acid is believed to have a catalytic effect on the process of the peptide bond formation by serving as an anchor which holds the reactants in place at the transition state [6]. However, this is questionable since it is more favorable for this hydrogen to act as a proton shuttle to the 3 0 leaving group [18]. In fact, this bond is the main reason for the 10 13 -fold reduction in the rate of peptide bond formation in that study compared to those in empirical studies [2]. It is proposed by Sievers et al. that the role of ribosomal bases is to lower the entropy of activation for the peptide bond formation. As reported in their study, the presence of ribosome results in a 10 4 -fold enhancement in the rate of peptide bond formation compared to the one carried out in solution (Table 2). The difference in activation entropy between the catalyzed (i.e. with ribosome) and uncatalyzed reactions, DDS à (ribosome water), is quite high, indicating the role of ribosome in catalyzing the reaction via the entropy of substrates. These results are also in good agreement with those obtained computationally using MD simulation by Trobro and Aqvist [1]. Although the reaction rate constant in their study is almost 10 26 -fold higher (Table 2), compared to our study, the enthalpy of ribosomal catalyzed peptide bond formation is not favorable (Table 3). Thus, the high rate of peptide bond formation in their study is due to more favorable entropy compared to our study. These results are in good agreement with the Sievers et al. s argument for the catalytic role of the ribosome during peptide bond formation. The argument concerning the catalytic role of the ribosome in substrate stabilization is further supported by comparing the rate of reaction in our study and that of Gindulyte et al. s. Although the DG of the reaction in our study is more favorable ( 3.9595 kcal/mol compared to 3.2 kcal/mol), the E a in Gindulyte et al. s study is lower resulting in a higher reaction rate constant. The presence of frozen ribosomal bases around the Gindulyte et al. s structure has resulted in an estimated 45 rotation of the Table 1 The comparison of the transition state coordinates between our study and Gindulyte et al. [6] Model Bond name Bond type Distance (Å) Optimized transition structure in free space (this study) r N C Forming 1.571 r C O Breaking 1.812 r O H Forming 1.281 r N H Breaking 1.198 r O H 1.821 Optimized transition structure in a frozen ribosomal environment (Gindulyte et al. [6]) r N C Forming 1.577 r C O Breaking 1.912 r O H Forming 1.395 r N H Breaking 1.167 r Catalytic Catalyzing 1.879

H. Monajemi et al. / Computational and Theoretical Chemistry 976 (2011) 148 152 151 Fig. 3. The reaction profile for the peptide bond formation. Table 2 The calculated rate of peptide bond formation in different studies. Study Model E a (kcal/mol) k (s 1 ) Our study Inhibitory H-bond 53.1 10 26 Gindulyte et al. [6] Catalytic H-bond 35.5 10 13 Trobro and Aqvist [1] Ribosomal active site 17.5 1 Sievers et al. [2] Ribosomal active site 16.5 5 Water solution 22.2 10 4 Table 3 The calculated values of enthalpy, entropy and free energy of the reaction in our study and that of Trobro and Aqvist [1]. Study DG (kcal/mol) DH (kcal/mol) DS (kcal/mol K) Our study 3.9595 8.0572 0.0137 Trobro and Aqvist [1] 9 10 0.0637 substrate around the 2-fold symmetry axis before the transition structure is formed. This rotation is not observed in our study. In order to investigate this process in detail, we have calculated the intrinsic reaction coordinate (IRC) of the process from reactants via the transition state through to the products. The optimized transition structure of this reaction is used as an input for the IRC calculation in both directions of change (i.e. from the transition state to both the reactants and products). Fig. 4 shows the variation of the total energy along the reaction path. The reaction starts from the positive reaction coordinate (i.e. reactants) towards the maximum energy of the transition state. Following the IRC path, it is observed that there is a very little change in the x dihedral angle i.e. between C a C 0 N C a (Fig. 2) as the peptide bond forms and the reaction moves towards the products (Fig. 5). This is a backbone dihedral angle that controls the distance between the two C a in the adjacent amino acids. This distance is normally 3:8 Å for a typical trans (x = 180 ) structure [9] and 2:9 Å for a rare cis (x =0 ) structure [16] in a polypeptide chain. Since this distance is 3 Å in our structure after the formation of the peptide bond, the structure should be in a cis form. Thus, the x is expected to move towards 0. However, as observed in Fig. 5, the x remains at almost 6 as the peptide bond forms. As shown in Fig. 2, the torsion of x towards any direction requires the rotation of atoms attached to the N and C 0. This rotation Fig. 4. The IRC path for the peptide bond formation. The total energy of the system is in the minimum point after formation of the product.

152 H. Monajemi et al. / Computational and Theoretical Chemistry 976 (2011) 148 152 Fig. 5. The variation of the omega dihedral angle with respect to the reaction coordinate. involves the oxygen atom which is attached to the C 0. However, this oxygen has formed a hydrogen bond with the 2 0 hydrogen of the hydroxyl group of its own ribose. This hydrogen bond, which limits the oxygen s movement towards the right angle, is different from the one which has been observed in the Gindulyte et al. s study. Although both are formed between the 2 0 hydroxyl group of the P-site adenosine and the oxygen attached to the C 0, one is formed with the oxygen of the A-site amino acid (Gindulyte et al.), and the other is formed with the oxygen of the P-site amino acid (our study). The former does not restrict the P-site amino acid s movement since it is attached to the carbon which is not involved in the x dihedral. However, the latter has an inhibitory effect on the movement of the P-site amino acid, not allowing it to have a proper rotation towards equilibrium, and resulting in a high activation barrier. On the other hand, the formation of the catalytic H-bond during the transition state of the reaction in the Gindulyte et al. s study facilitates this rotation towards proper substrate stabilization [6]. 4. Conclusion Despite the overall unfavorable free energy for the peptide bond formation in Gindulyte et al. s study, its 10 13 -fold enhancement for the rate of reaction compared to our study indicates the importance of presence of ribosomal bases. This is mainly due to the favorable reaction entropy in Gindulyte et al. s study. The favorable entropy and unfavorable enthalpy in experimental studies as compared to our study is also indicative of the importance of substrate stabilization in facilitating the formation of peptide bonds. 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